Advances in Colloid and Interface Science 208 (2014) 214–224 Contents lists available at ScienceDirect Advances in Colloid and Interface Science journal homepage: www.elsevier.com/locate/cis Wrapping of nanoparticles by membranes Amir H. Bahrami a, Michael Raatz a, Jaime Agudo-Canalejo a, Raphael Michel b, Emily M. Curtis c, Carol K. Hall c, Michael Gradzielski b, Reinhard Lipowsky a,ThomasR.Weikla,⁎ a Max Planck Institute of Colloids and Interfaces, Department of Theory and Bio-Systems, Science Park Golm, 14424 Potsdam, Germany b Stranski-Laboratorium für Physikalische und Theoretische Chemie, Institut für Chemie, Technische Universität Berlin, 10623 Berlin, Germany c Department of Chemical and Biomolecular Engineering, North Carolina State University, Engineering Building I, 911 Partners Way, Raleigh, NC 27695-7905, USA article info abstract Available online 12 March 2014 How nanoparticles interact with biomembranes is central for understanding their bioactivity. Biomembranes wrap around nanoparticles if the adhesive interaction between the nanoparticles and membranes is sufficiently Keywords: strong to compensate for the cost of membrane bending. In this article, we review recent results from theory and Nanoparticles simulations that provide new insights on the interplay of bending and adhesion energies during the wrapping of Membranes nanoparticles by membranes. These results indicate that the interplay of bending and adhesion during wrapping Bending energy is strongly affected by the interaction range of the particle–membrane adhesion potential, by the shape of the nanoparticles, and by shape changes of membrane vesicles during wrapping. The interaction range of the particle–membrane adhesion potential is crucial both for the wrapping process of single nanoparticles and the cooperative wrapping of nanoparticles by membrane tubules. © 2014 Elsevier B.V. All rights reserved. Contents 1. Introduction.............................................................. 214 2. Interplayofelasticandadhesiveenergiesduringwrapping......................................... 215 3. Wrappingofsphericalparticles..................................................... 215 3.1. Contact potential with range ρ =0................................................ 215 3.2. Particle membrane interaction potentials with nonzero range ρ ................................... 216 4. Wrappingofnon-sphericalparticles................................................... 217 4.1. Fullwrappingofellipsoidalparticles................................................ 217 4.2. Orientationalchangesofellipsoidalparticlesduringwrapping.................................... 218 5. Internalizationofparticlesbyvesicles.................................................. 219 5.1. Presenceofosmoticallyactiveparticles.............................................. 219 5.2. Absenceofosmoticallyactiveparticles............................................... 220 6. Cooperativewrappingofnanoparticles.................................................. 220 7. Discussion............................................................... 222 Acknowledgments.............................................................. 223 References................................................................. 223 1. Introduction are frequently incorporated into smart materials, in food packing, as anti- fouling agents or to keep surfaces sterile [7]. This wide application of in- Recent advances in nanotechnology have led to an increasing inter- dustrial nanoparticles has also led to concerns about their safety [8,9,3] est in how nanoparticles interact with living organisms [1]. On the one and has triggered intense activities to investigate and understand hand, biomedically designed nanoparticles are promising delivery vehi- nanotoxicity [10–12]. cles or vectors in drug treatments [2–6]. On the other hand, nanoparticles Since nanoparticles have to cross biomembranes to enter the cells and organelles of living organisms, a current focus is on understanding ⁎ Corresponding author. the interactions of nanoparticles with membranes. Nanoparticles that E-mail address: [email protected] (T.R. Weikl). are larger than the membrane thickness cross the membrane by http://dx.doi.org/10.1016/j.cis.2014.02.012 0001-8686/© 2014 Elsevier B.V. All rights reserved. A.H. Bahrami et al. / Advances in Colloid and Interface Science 208 (2014) 214–224 215 wrapping and subsequent fission of a membrane neck. The wrapping of ofthemembranetensionσ and area A. The adhesion energy of a particle nanoparticles by the membranes can either occur spontaneously from can be written as the integral an interplay of adhesive and elastic energies, or can be assisted by the Z curvature-inducing proteins and protein machineries of cellular mem- E ¼ VdðÞdA ð3Þ branes [13–16]. ad The topic of this review is the spontaneous wrapping of nanoparti- cles by membranes. Spontaneous wrapping occurs if the adhesive inter- over the membrane area A where V(d) is the particle–membrane inter- action between the nanoparticles and the membrane is sufficiently action potential, and d is the local distance of the membrane from the strong to compensate for the cost of membrane bending. The spontane- particle surface. The particle–membrane interaction may either result ous wrapping of nanoparticles has been observed in experiments with from electrostatic and Van der Waals interactions between the lipid bilay- lipid vesicles [17–21], polymersomes [22,23],andcells[24,25],and er and the particles, or may be mediated by the specific binding of recep- has been investigated by theoretical calculations [26–39] and simula- tor and ligand molecules that are anchored in the membrane and to the tions [40–62]. In this review article, our focus is on recent results from particle surface (see Section 7 for a more detailed discussion). The total theory and simulations that provide new insights on how the wrapping energy that governs the wrapping process is the sum process is affected (i) by the interaction range of the particle– ¼ þ þ ð Þ membrane adhesion potential, (ii) by the shape of the nanoparticles, E Ebe Ete Ead 4 and (iii) by shape changes of membrane vesicles during wrapping. Previous theoretical investigations have been largely focused on of the elastic energy of the membrane and the adhesion energy of the particle–membrane adhesion potentials with an interaction range that particles. is negligibly small compared to the particle dimensions. For nanoparti- The wrapping process described by the total energy in Eq. (4) cles, however, the interaction range of the adhesion potential can be sev- depends on several length scales. These length scales are characteristic eral percent of the particle diameter. Such interaction ranges strongly lengths (i) of the membrane, (ii) of the particles, and (iii) of the parti- affect the wrapping process of single particles (see Section 3) and can cle–membrane interaction. The characteristic length of the particle– lead to the cooperative wrapping of particles in tubular membrane invag- membrane interaction is the range ρ of this interaction. Characteristic inations (see Section 6) [39]. These particle-filled membrane tubes have length scales of the membrane arepffiffiffiffiffiffiffiffiffi the inverse spontaneous curvature been recently observed by several groups in simulations [48,50,53]. 1/co and the ‘crossover length’ κ=σ . On length scales smaller than Experiments indicate that the internalization of nanoparticles by this crossover length, the elastic energy Eel = Ebe + Ete of the membrane cells is affected by the size and shape of the particles [63–69,46, is dominated by the bending energy Ebe. On length scales larger than the 70–73]. How the spontaneous wrapping of nanoparticles depends on crossover length, the tension contribution Ete dominates over the bending the particle shape has been investigated in recent simulations [46,45, energy Ebe. For membrane vesicles, an additional characteristic length is 52,55,54,58,61,56,74]. In general, the bending energy cost for wrapping the square root of the membrane area Ap. strongly depends on the shape of nanoparticles (see Section 4). The In this review, we focus on wrapping scenarios in which the charac- interplay of bending and adhesion energies can induce orientational teristic lengths of the particles are small comparedpffiffiffiffiffiffiffiffiffi to the inverse sponta- changes of ellipsoidal particles relative to the membrane during wrap- neous curvature 1/co and to the crossover length κ=σ of the membrane. ping [55,56]. The spontaneous wrapping depends strongly on the parti- The spontaneous curvature co and tension contribution Ete then are cle size because the adhesion energy increases with the size of a particle. negligible in the elastic energy Eel of the membranes. These wrapping The bending energy cost of wrapping, in contrast, is independent of the scenarios are realistic in particular for small particles with characteristic particle size (see Section 4). Finally, the wrapping of particles by mem- dimensions of tens of nanometers. For typical values of the bending ri- κ σ brane vesicles can lead to shape changes of the vesicles that lower the gidity between 10 and 20 kBT [77] and a membranepffiffiffiffiffiffiffiffiffi tension of a bending energy of the vesicles and, thus, assist the wrapping process few μN/m [78], for example, the crossover length κ=σ adopts values (see Section 5). between 100 and 200 nm. In the next section, we start with a general discussion of the elastic and adhesive energies that are involved in the wrapping